Polynomial Calculator
Work with polynomials by entering their coefficients. Add, subtract or multiply two polynomials, differentiate or integrate one, evaluate it at a chosen value of x, or read off its degree. Coefficients are listed by power, so 1 + 2x + 3x^2 is entered as 1, 2, 3.
How to use the polynomial calculator
- Type the coefficients of each polynomial, lowest power first, separated by commas, so 1, 2, 3 means 1 + 2x + 3x squared.
- Pick an operation: add, subtract or multiply the two polynomials, or differentiate, integrate or read the degree of the first one.
- Read the result polynomial in standard form and, if you set a value for x, its value at that point.
Examples
Multiply two binomials
(1 + x) times (1 + x)
1 + 2x + x^2
Add two polynomials
(1 + 2x + 3x^2) + (1 + x)
2 + 3x + 3x^2
Evaluate at a point
1 + 2x + 3x^2 at x = 2
17
Frequently asked questions
How do I enter a polynomial?
List the coefficients in order of increasing power, separated by commas. The first number is the constant term, the next is the coefficient of x, then x squared, and so on. For example 1 + 2x + 3x squared is entered as 1, 2, 3, and 5x squared on its own is 0, 0, 5.
Which operations are supported?
You can add, subtract and multiply two polynomials, and differentiate, integrate or find the degree of one. The calculator also evaluates a polynomial at any value of x and shows the result in standard form, highest power first.
How is the polynomial evaluated?
Evaluation uses Horner's method, which rewrites the polynomial so it needs only one multiplication and one addition per term. This is fast and keeps rounding error small compared with computing each power separately.
What does the degree mean and what happens with the zero polynomial?
The degree is the highest power that has a non-zero coefficient, so 1 + 2x + 3x squared has degree 2. Trailing zero coefficients are ignored. The zero polynomial has no leading term, so its degree is reported as negative infinity.
Why did some terms disappear from my answer?
When coefficients cancel, for example adding 1 + x to 1 minus x, the x terms sum to zero and are removed so the result is just the constant 2. Terms with a zero coefficient are never shown in the formatted output.
Is my data private?
Yes. Every calculation runs entirely in your browser. The coefficients you type are never uploaded or stored on a server, so your work stays on your own device.
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